A typical radar system includes a powerful transmitter and sensitive receiver normally connected to the same antenna. After producing a brief pulse of radio signal, the transmitter is turned off for the receiver to receive the reflections of pulse signal off distant targets. Thus, the radar receives a return signal that is a superposition of reflections from each target, each reflection being a time delayed and scaled version of the transmitted pulse. In a simple realization, the transmitted pulse is simply a constant amplitude and frequency sinusoid that is rapidly switched on and off. This is commonly referred to as a CW (continuous wave) pulse. However, this waveform has significant limitations. If the range difference between two targets is small enough that the difference in their reflection delays is less than the pulse duration, their reflections will overlap and the radar will not be able to resolve them as separate targets. Thus, it is desirable to make the pulse duration as short as possible. Moreover, the maximum range at which a target is detectable depends on the energy transmitted in the pulse, which is proportional to the product of the pulse amplitude and pulse duration. Thus if pulse duration is decreased, pulse amplitude must be increased to maintain detection range, but there are practical limitations to how much amplitude (and corresponding transmit power) can be increased.
An alternative approach is to transmit a relatively long pulse, but to modulate it in some way. This allows closely separated targets to be resolved even though their reflections overlap by means of appropriate signal processing. Such techniques are generically referred to as pulse compression, since in effect they compress a long duration modulated pulse to provide resolution comparable to a much shorter CW pulse. A commonly used pulse compression technique employs a matched filter (MF) technique, in which, a replica of the transmitted pulse is correlated with the return signal over the range of potential target delays. This processing produces a signal consisting of delayed and scaled versions of the transmitted pulse autocorrelation function (where the delays correspond to the round-trip propagation time for each target and the scaling depends on the reflection strength for each target), plus random background noise. Thus, by choosing a transmit waveform having an autocorrelation function, that is a narrow pulse, the matched filter output produces signal spikes corresponding to target ranges.
An ideal transmit waveform would have an impulse autocorrelation function with a finite value at zero delay, and zero elsewhere). However, such a waveform is not physically realizable and practical waveforms only approximate this ideal to various degrees. A commonly used example is the FM chirp, in which, frequency is linearly swept over time. This produces an autocorrelation function such as illustrated in FIG. 1A, which has a strong peak (or main lobe) surrounded by smaller peaks (side lobes) whose amplitudes rapidly decay away from the main lobe.
Another alternative is to use a pseudo-random noise (P-N) pulse, in which, a pseudo-random noise process is used to vary the amplitude and phase of a sinusoidal carrier wave. FIG. 1B shows an example autocorrelation function for such a random phase waveform. Like the FM chirp, this autocorrelation technique has a strong main lobe peak, but the side lobes remain more uniformly high away from the main lobe. This means that weaker targets may be buried in the side lobes of stronger targets, even if range (delay) separation between them is large. Despite this, using P-N may still be desirable, for instance, to make detection of the radar signal by hostile observers more difficult.
Another factor to consider is that targets and/or the radar may be in motion, so that target range may be changing at a non-zero rate. This results in a Doppler shift, i.e., a difference between the frequencies of the transmitted signal and the received target reflection. Absent compensation, this Doppler shift may degrade MF performance, since the Doppler effectively adds frequency modulation that de-correlates the return signal. Thus, some means of estimating and compensating Doppler frequency is desirable. In addition, Doppler estimates provide useful information in their own right, since they indicate the rate at which target range is opening or closing. Consequently, the problem of jointly estimating range and Doppler for a multiplicity of targets is of key importance in many radar systems.
Moreover, in modem radar systems with multiple target detection capability, high sidelobe levels of strong targets or clutter can mask the presence of weaker targets in the range-Doppler space. This problem is worsened when using non-standard radar waveforms (e.g. P-N sequences) since the masking problem is exacerbated by use of non-standard waveforms, with poor sidelobe properties and Doppler intolerance.
There have been many approaches to estimate range-Doppler of radar returns. For example, Doppler compensated matched filters are commonly used. However, the effectiveness of this approach depends on the transmit waveform autocorrelation properties, for example, the uniformly high range side-lobes associated with P-N waveforms limit the ability to detect weak targets in the presence of strong targets. Also, since the weights of the matched filters need to be dynamically adjusted, a complex and costly computation is needed. Various minimum mean square error (MMSE) algorithms have been proposed to mitigate these range side-lobes. These algorithms postulate a mathematical model, that is, a function that maps certain unknown input variables (such as target delay, Doppler, and amplitude) to a model output that predicts the actual observed data. Because of random measurement errors the actual observations generally do not exactly match the model outputs, even if the inputs are correct.
A more recently developed single pulse imaging (SPI) method explicitly considers both Doppler and range estimation. However, this method is limited by the assumption that the number of transmit pulse samples is substantially less than the number of range bins. The SPI method also requires a series of matrix inversion operations with dimension equal to the transmit pulse sample length, which are also computationally intensive and complex.
Accordingly, there is a need for a more efficient, less computationally complex, and higher quality approach to estimate range-Doppler of radar returns, especially, when the radar waveforms are non-traditional or arbitrary radar waveforms.